A Study of Nonlinear Behavior of Flexible Tool and Workpiece in Turning Operation With Regenerative Effect Under Internal and Primary Resonance Conditions

Abstract

In this work, the nonlinear dynamic behavior of turning operation has been studied considering flexible tool and thin cylindrical workpiece. The system is taken as a two-degree-of-freedom system with nonlinear stiffness and is subjected to self-excited vibration because of the regenerative effect. The cutting force is considered to be a combination of a constant and periodic force in addition to the force due to the regenerative effect. The regenerative effect during turning operation is included in the mathematical model, resulting in a nonlinear delay differential equation. Here, the natural frequency of the workpiece is assumed to be closed to that of the tool, leading to 1:1 internal resonance. Further, the frequency of the time-varying cutting force is assumed to be closed to the natural frequency of the workpiece giving rise to primary resonance condition. The nonlinear responses and the stability of the tool and the workpiece have been determined using a higher-order method of multiple scales (MMS) under internal and primary resonance conditions. The solution of the equation of motion using the MMS is validated by comparing the solution obtained using the numerical method. The effect of the tool and workpiece stiffness nonlinearities on steady-state frequency responses and stability is investigated, and system parameters are also identified to have stable turning operation. This work will find applications in estimating the system parameters for chatter-free turning operation with a flexible tool and workpiece when their dynamic compliances are comparable.